Abundance of 3-Planes on Real Projective Hypersurfaces

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FİNASHİN S., Kharlamov V.

Arnold Mathematical Journal, vol.1, no.2, pp.171-199, 2015 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1007/s40598-015-0015-5
  • Journal Name: Arnold Mathematical Journal
  • Journal Indexes: Scopus
  • Page Numbers: pp.171-199
  • Keywords: Enumerative geometry, Real algebraic geometry, Real Schubert calculus
  • Middle East Technical University Affiliated: Yes


© 2015, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.We show that a generic real projective n-dimensional hypersurface of odd degree d, such that 4(n-2)=(d+33), contains “many” real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, d3log d, as the number of complex 3-planes. This estimate is based on the interpretation of a suitable signed count of the 3-planes as the Euler number of an appropriate bundle.